Generally, discrete cosine transforms have been most widely used in image and digital speech processing where a good transform performance, as disclosed in Digital Picture Processing, Second Edition, Volume 1, pp. 159-168, by Azriel Rosenfeld and Avinash C. Kak, 1982, is required. However, the transform must process a large quantity of data and, therefore, is time consuming.
In order to solve the problem, many kinds of fast algorithms for discrete cosine transforms have been developed, such as, "A Simple Discrete Cosine Transform Systolic Array based on DFT for Video Code c", by Jong-oh Park, Kwang-jae Lee, Guen-ho Yang, Ju-yong Park and Moon-ho Lee, on Nov. 1989 in Korea. However, in the digital image processing field, fast algorithms have short-comings in that real-time applications or hardware implementations of the algorithms are very complicated.